Reflectional topology in MV-algebras

Document Type : Research Paper

Authors

1 Faculty of Mathematics and computing, Higher Education Complex of Bam, Kerman, Iran.

2 Department of Pure Mathematics, Faculty of Math and Computers, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

In this paper, we define soaker ideals in an MV-algebra, and study the relationships between soaker ideals and the other ideals in an involutive MV -algebras. Then we introduce a topology on the set of all the soaker ideals, which we call reflectional topology, and give a basis for it. By defining the notion of join-soaker ideals, we show that the reflectional topology is compact. We also give a characterization of connectedness of the reflectional topology. Finally, we investigate the properties of T0 and T1-space in this topology.

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Categories and General Algebraic Structures with Applications
Volume 16, Issue 1
January 2022
Pages 249-267

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